Approximate Controllability for Nonlinear Evolution Hemivariational Inequalities in Hilbert Spaces

2015 ◽  
Vol 53 (5) ◽  
pp. 3228-3244 ◽  
Author(s):  
Zhenhai Liu ◽  
Xiuwen Li ◽  
Dumitru Motreanu
Keyword(s):  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Nonlinear Evolution ◽  
Hemivariational Inequalities ◽  
Evolution Hemivariational Inequalities

scholarly journals Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

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